The rapid proliferation of Internet of Things devices introduces significant challenges in determining optimal service placement across heterogeneous computing layers, spanning from centralized cloud servers to decentralized fog and edge nodes. Effective placement is essential to minimize latency, reduce energy consumption, and control costs, all while adhering to resource constraints such as limited memory and processing capacity. In this paper, we investigate several strategies for solving the IoT service placement problem. To overcome the limited adaptability of traditional optimization approaches, we introduce dynamic resource management in the simulation environment YAFS and propose a Deep Reinforcement Learning–based approach utilizing a Double Deep Q-Network (DDQN) architecture. The DRL agent autonomously learns placement policies through continuous interaction with the environment, optimizing a weighted multi-objective reward that balances execution time, energy efficiency, and cost. Experimental evaluations were conducted under two scenarios: memory-only constraints and combined memory plus CPU constraints. Results demonstrate that the DRL-based strategy consistently outperforms baseline approaches, including three meta-heuristic optimization methods—Genetic Algorithm, Simulated Annealing, and Tabu Search—as well as the cloud-only strategy, across all performance metrics.